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We present a review of the Sachdev-Ye-Kitaev (SYK) model of compressible quantum many-body systems without quasiparticle excitations, and its connections to various theoretical studies of non-Fermi liquids in condensed matter physics. The review is placed in the context of numerous experimental observations on correlated electron materials. Strong correlations in metals are often associated with their proximity to a Mott transition to an insulator created by the local Coulomb repulsion between the electrons. We explore the phase diagrams of a number of models of such local electronic correlation, employing a dynamical mean field theory in the presence of random spin exchange interactions. Numerical analyses and analytical solutions, using renormalization group methods and expansions in large spin degeneracy, lead to critical regions which display SYK physics. The models studied include the single-band Hubbard model, the $t$-$J$ model and the two-band Kondo-Heisenberg model in the presence of random spin exchange interactions. We also examine non-Fermi liquids obtained by considering each SYK model with random four-fermion interactions to be a multi-orbital atom, with the SYK-atoms arranged in an infinite lattice. We connect to theories of sharp Fermi surfaces without any low-energy quasiparticles in the absence of spatial disorder, obtained by coupling a Fermi liquid to a gapless boson; a systematic large $N$ theory of such a critical Fermi surface, with SYK characteristics, is obtained by averaging over an ensemble of theories with random boson-fermion couplings. Finally, we present an overview of the links between the SYK model and quantum gravity and end with an outlook on open questions., 72 pages, 25 figures and lots of references. Comments are welcome; (v2) Added references

Twisted van der Waals heterostructures have latterly received prominent attention for their many remarkable experimental properties, and the promise that they hold for realising elusive states of matter in the laboratory. We propose that these systems can, in fact, be used as a robust quantum simulation platform that enables the study of strongly correlated physics and topology in quantum materials. Among the features that make these materials a versatile toolbox are the tunability of their properties through readily accessible external parameters such as gating, straining, packing and twist angle; the feasibility to realize and control a large number of fundamental many-body quantum models relevant in the field of condensed-matter physics; and finally, the availability of experimental readout protocols that directly map their rich phase diagrams in and out of equilibrium. This general framework makes it possible to robustly realize and functionalize new phases of matter in a modular fashion, thus broadening the landscape of accessible physics and holding promise for future technological applications., Comment: Invited to Nature Physics

International audience; COSMO ("Communicating Objects by Sensory-Motor Operations") is a framework for jointly modeling speech perception and production by considering sensory-motor relations as a core component of its program. COSMO allows to jointly formalize two major theoretical frameworks in speech research that are auditory and motor theories – but also to integrate them within perceptual-motor theories. This leads to new perception models associating auditory processing and motor knowledge, and new speech motor control models oriented toward the achievement of multimodal sensory goals. We present the main results obtained with COSMO, and perspectives about temporal processing and deep learning implementation allowing to get closer to learning on real data.; Nous avons développé un cadre de modélisation des processus de la communication parlée, COSMO (« Communicating Objects by Sensory-Motor Operations »), qui s'applique à la fois aux modèles de perception et de production de parole en installant les relations sensori-motrices au coeur de son programme. COSMO permet de formaliser conjointement deux cadres théoriques majeurs des recherches sur la communication parlée, les théories auditives et motrices-mais aussi de les intégrer au sein de théories perceptuo-motrices. Ceci conduit ainsi à de nouveaux modèles de perception alliant traitements auditifs et prise en compte de connaissances motrices, ou de nouveaux modèles de contrôle moteur de la parole orientés vers la réalisation de buts sensoriels multimodaux. Nous présentons ces avancées ainsi que des pistes de développement sur le traitement temporel et l'implémentation deep learning permettant d'aller vers l'apprentissage sur des données réelles.

We numerically study a model of interacting spin-$1/2$ electrons with random exchange coupling on a fully connected lattice. This model hosts a quantum critical point separating two distinct metallic phases as a function of doping: a Fermi liquid phase with a large Fermi surface volume and a low-doping phase with local moments ordering into a spin-glass. We show that this quantum critical point has non-Fermi liquid properties characterized by $T$-linear Planckian behavior, $\omega/T$ scaling and slow spin dynamics of the Sachdev-Ye-Kitaev (SYK) type. The $\omega/T$ scaling function associated with the electronic self-energy is found to have an intrinsic particle-hole asymmetry, a hallmark of a `skewed' non-Fermi liquid., Comment: 6+11 pages; 4+10 figures; v2. improves data analysis, expands appendix, increases convergence of data, updates all figures

Significance In “Planckian metals,” electrons dissipate energy at the fastest possible rate allowed by the fundamental laws of quantum mechanics, resulting in a linear temperature dependence of their electrical resistivity. Although observed for a number of quantum materials, this phenomenon lacks a general theoretical understanding and is often considered as one of the prominent fundamental questions in condensed matter physics. Here, we show that Planckian dissipation and a behavior consistent with the “marginal Fermi liquid” phenomenology emerge in the quantum critical regime separating a Mott insulating spin glass and a Fermi liquid. By establishing this behavior in an explicit model solvable by state-of-the-art computational methods, our theory paves the way toward a deeper understanding of Planckian or “strange” metals., “Strange metals” with resistivity depending linearly on temperature T down to low T have been a long-standing puzzle in condensed matter physics. Here, we consider a lattice model of itinerant spin-1/2 fermions interacting via onsite Hubbard interaction and random infinite-ranged spin–spin interaction. We show that the quantum critical point associated with the melting of the spin-glass phase by charge fluctuations displays non-Fermi liquid behavior, with local spin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. This extends the quantum spin liquid dynamics previously established in the large-M limit of SU(M) symmetric models to models with physical SU(2) spin-1/2 electrons. Remarkably, the quantum critical regime also features a Planckian linear-T resistivity associated with a T-linear scattering rate and a frequency dependence of the electronic self-energy consistent with the marginal Fermi liquid phenomenology.

Interface quantum materials have yielded a plethora of previously unknown phenomena, including unconventional superconductivity, topological phases, and possible Majorana fermions. Typically, such states are detected at the interface between two insulating constituents by electrical transport, but whether either material is conducting, transport techniques become insensitive to interfacial properties. To overcome these limitations, we use angle-resolved photoemission spectroscopy and molecular beam epitaxy to reveal the electronic structure, charge transfer, doping profile, and carrier effective masses in a layer-by-layer fashion for the interface between the Dirac nodal-line semimetal SrIrO

Thin films of the solid solution Nd 1 − x La x NiO3 are grown in order to study the expected 0 K phase transitions at a specific composition. We experimentally map out the structural, electronic and magnetic properties as a function of x and a discontinuous, possibly first order, insulator–metal transition is observed at low temperature when x = 0.2. Raman spectroscopy and scanning transmission electron microscopy show that this is not associated with a correspondingly discontinuous global structural change. On the other hand, results from density functional theory (DFT) and combined DFT and dynamical mean field theory calculations produce a 0 K first order transition at around this composition. We further estimate the temperature-dependence of the transition from thermodynamic considerations and find that a discontinuous insulator–metal transition can be reproduced theoretically and implies a narrow insulator–metal phase coexistence with x. Finally, muon spin rotation (µSR) measurements suggest that there are non-static magnetic moments in the system that may be understood in the context of the first order nature of the 0 K transition and its associated phase coexistence regime.

We present a fully charge self-consistent implementation of dynamical mean field theory (DMFT) combined with density functional theory (DFT) for electronic structure calculations of materials with strong electronic correlations. The implementation uses theQuantum ESPRESSOpackage for the DFT calculations, theWannier90code for the up-/down-folding and theTRIQSsoftware package for setting up and solving the DMFT equations. All components are available under open source licenses, are MPI-parallelized, fully integrated in the respective packages, and use an hdf5 archive interface to eliminate file parsing. We show benchmarks for three different systems that demonstrate excellent agreement with existing DFT + DMFT implementations in otherab initioelectronic structure codes., Journal of Physics: Condensed Matter, 34 (23), ISSN:0953-8984, ISSN:1361-648X

International audience; We consider non-Fermi liquids in which the inelastic scattering rate has an intrinsic particle-hole asymmetry and obeys ω/T scaling. We show that, in contrast to Fermi liquids, this asymmetry influences the low-temperature behavior of the thermopower even when the impurity scattering dominates. Implications for the unconventional sign and temperature dependence of the thermopower in cuprates in the strange metal (Planckian) regime are emphasized.

This Perspective addresses the design, creation, characterization and control of synthetic quantum materials with strong electronic correlations. We show how emerging synergies between theoretical/computational approaches and materials design/experimental probes are driving recent advances in the discovery, understanding and control of new electronic behaviour in materials systems with interesting and potentially technologically important properties. The focus here is on transition metal oxides, where electronic correlations lead to a myriad of functional properties including superconductivity, magnetism, Mott transitions, multiferroicity and emergent behaviour at picoscale-designed interfaces. Current opportunities and challenges are also addressed, including possible new discoveries of non-equilibrium phenomena and optical control of correlated quantum phases of transition metal oxides. This Perspective addresses the properties of strongly correlated materials, with a particular focus on computational, synthetic and spectroscopic approaches.

The physics of the triangular lattice Hubbard model exhibits a rich phenomenology, ranging from a metal-insulator transition, intriguing thermodynamic behavior, and a putative spin liquid phase at intermediate coupling, ultimately becoming a magnetic insulator at strong coupling. In this multimethod study, we combine a finite-temperature tensor network method, minimally entangled thermal typical states (METTS), with two Green-function-based methods, connected-determinant diagrammatic Monte Carlo and cellular dynamical mean-field theory, to establish several aspects of this model. We elucidate the evolution from the metallic to the insulating regime from the complementary perspectives brought by these different methods. We compute the full thermodynamics of the model on a width-four cylinder using METTS in the intermediate to strong coupling regime. We find that the insulating state hosts a large entropy at intermediate temperatures, which increases with the strength of the coupling. Correspondingly, and consistently with a thermodynamic Maxwell relation, the double occupancy has a minimum as a function of temperature which is the manifestation of the Pomeranchuk effect of increased localization upon heating. The intermediate coupling regime is found to exhibit both pronounced chiral as well as stripy antiferromagnetic spin correlations. We propose a scenario in which time-reversal symmetry-broken states compete with stripy-spin states at lowest temperatures., Comment: (23 pages, 18 figures)

The interplay between thermal and quantum fluctuations controls the competition between phases of matter in strongly correlated electron systems. We study finite-temperature properties of the strongly coupled two-dimensional doped Hubbard model using the minimally-entangled typical thermal states (METTS) method on width $4$ cylinders. We discover that a phase characterized by commensurate short-range antiferromagnetic correlations and no charge ordering occurs at temperatures above the half-filled stripe phase extending to zero temperature. The transition from the antiferromagnetic phase to the stripe phase takes place at temperature $T/t \approx 0.05$ and is accompanied by a step-like feature of the specific heat. We find the single-particle gap to be smallest close to the nodal point at $\mathbf{k}=(\pi/2, \pi/2)$ and detect a maximum in the magnetic susceptibility. These features bear a strong resemblance to the pseudogap phase of high-temperature cuprate superconductors. The simulations are verified using a variety of different unbiased numerical methods in the three limiting cases of zero temperature, small lattice sizes, and half-filling. Moreover, we compare to and confirm previous determinantal quantum Monte Carlo results on incommensurate spin-density waves at finite doping and temperature., Comment: 18 pages, 16 figures

The accurate estimation of band gaps of solid-state materials is of great relevance for modern optoelectronic, electronic, and photovoltaic applications. However, the precise $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ computation of accurate band gaps is a resource intensive task. In this article, inspired by the Hohenberg-Kohn theorem of density-functional theory, the authors demonstrate the possibility of explicitly parametrizing the mapping between the electron density in the unit cell and the corresponding experimental band gap in real materials using deep neural networks. The proposed data-driven approach achieves accuracies comparable to state of the art $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ approaches, at a much lower computational cost.

International audience; It is increasingly considered that human speech perception and production both rely on articulatory representations. In this paper, we investigate whether this type of representation could improve the performances of a deep generative model (here a variational autoencoder) trained to encode and decode acoustic speech features. First we develop an articulatory model able to associate articulatory parameters describing the jaw, tongue, lips and velum configurations with vocal tract shapes and spectral features. Then we incorporate these articulatory parameters into a variational autoencoder applied on spectral features by using a regularization technique that constrains part of the latent space to represent articulatory trajectories. We show that this articulatory constraint improves model training by decreasing time to convergence and reconstruction loss at convergence, and yields better performance in a speech denoising task.

We address the question of the degree of spatial nonlocality of the self-energy in the iron-based superconductors, a subject which is receiving considerable attention. Using LiFeAs as a prototypical example, we extract the self-energy from angular-resolved photoemission spectroscopy data. We use two distinct electronic structure references: density functional theory in the local density approximation and linearized quasiparticle self-consistent GW (LQSGW). We find that with the LQSGW reference, spatially local dynamical correlations provide a consistent description of the experimental data, and account for some surprising aspects of the data such as the substantial out-of-plane dispersion of the electron Fermi surface having dominant $xz/yz$ character. Hence, correlations effects can be separated into static nonlocal contributions well described by LQSGW and dynamical local contributions. Hall effect and resistivity data are shown to be consistent with this description.

We present a comprehensive dynamical mean field study of the triangular lattice moir\'e Hubbard model, which is believed to represent the physics of moir\'e bilayer transition metal dichalcogenides. In these materials, important aspects of the band structure including the bandwidth and the order and location of van Hove singularities can be tuned by varying the interlayer potential. We present a magnetic and metal-insulator phase diagram and a detailed study of the dependence of the resistivity on temperature, band filling and interlayer potential. We find that transport displays Fermi liquid, strange metal and quantum critical behaviors in distinct regions of the phase diagram. Specifically, we find that the cube-root van Hove singularity ($\rho(\epsilon) \sim|\epsilon|^{-1 / 3}$) gives a strange metal behavior with a $T$-linear scattering rate and $\omega/T$ scaling. We show how magnetic order affects the resistivity. Our results elucidate the physics of the correlated states and the metal-insulator continuous transition recently observed in twisted homobilayer WSe$_2$ and heterobilayer MoTe$_2$/WSe$_2$ experiments., Comment: 12 pages, 11 figures

We introduce a systematically improvable family of variational wave functions for the simulation of strongly correlated fermionic systems. This family consists of Slater determinants in an augmented Hilbert space involving "hidden" additional fermionic degrees of freedom. These determinants are projected onto the physical Hilbert space through a constraint which is optimized, together with the single-particle orbitals, using a neural network parametrization. This construction draws inspiration from the success of hidden particle representations but overcomes the limitations associated with the mean-field treatment of the constraint often used in this context. Our construction provides an extremely expressive family of wave functions, which is proven to be universal. We apply this construction to the ground state properties of the Hubbard model on the square lattice, achieving levels of accuracy which are competitive with and in some cases superior to state-of-the-art computational methods.

We present exact diagonalization results on finite clusters of a $t$-$J$ model of spin-1/2 electrons with random all-to-all hopping and exchange interactions. We argue that such random models capture qualitatively the strong local correlations needed to describe the cuprates and related compounds, while avoiding lattice space group symmetry breaking orders. The previously known spin glass ordered phase in the insulator at doping $p=0$ extends to a metallic spin glass phase up to a transition $p=p_c \approx 1/3$. The dynamic spin susceptibility shows signatures of the spectrum of the Sachdev-Ye-Kitaev models near $p_c$. We also find signs of the phase transition in the entropy, entanglement entropy and compressibility, all of which exhibit a maximum near $p_c$. The electron energy distribution function in the metallic phase is consistent with a disordered extension of the Luttinger-volume Fermi surface for $p>p_c$, while this breaks down for $p, Comment: 5 pages, 4 figures

The nonlinear optical response of an excitonic insulator coupled to lattice degrees of freedom is shown to depend in strong and characteristic ways on whether the insulating behavior originates primarily from electron-electron or electron-lattice interactions. Linear response optical signatures of the massive phase mode and the amplitude (Higgs) mode are identified. Upon nonlinear excitation resonant to the phase mode, a new in-gap mode at twice the phase mode frequency is induced, leading to a huge second harmonic response. Excitation of in-gap phonon modes leads to different and much smaller effects. A Landau-Ginzburg theory analysis explains these different behaviors and reveals that a parametric resonance of the strongly excited phase mode is the origin of the photoinduced mode in the electron-dominant case. The difference in the nonlinear optical response serves as a measure of the dominant mechanism of the ordered phase.

Distortions of the oxygen octahedra influence the fundamental electronic structure of perovskite oxides, such as their bandwidth and exchange interactions. Utilizing a fully ab-initio methodology based on density functional theory plus dynamical mean field theory (DFT+DMFT), we study the crystal and magnetic structure of SrMoO$_3$. Comparing our results with DFT+$U$ performed on the same footing, we find that DFT+$U$ overestimates the propensity for magnetic ordering, as well as the octahedral rotations, leading to a different ground state structure. This demonstrates that structural distortions can be highly sensitive to electronic correlation effects, and to the considered magnetic state, even in a moderately correlated metal such as SrMoO$_3$. Moreover, by comparing different downfolding schemes, we demonstrate the robustness of the DFT+DMFT method for obtaining structural properties, highlighting its versatility for applications to a broad range of materials., 11 pages, 10 figures

The hemocyanin protein binds and transports molecular oxygen via two copper atoms at its core. The singlet state of the $${{\rm{Cu}}}_{2}{{\rm{O}}}_{2}$$ Cu 2 O 2 core is thought to be stabilised by a superexchange pathway, but detailed in situ computational analysis is complicated by the multi-reference character of the electronic ground state. Here, electronic correlation effects in the functional site of hemocyanin are investigated using a novel approach, treating the localised copper 3d electrons with cluster dynamical mean field theory. This enables us to account for dynamical and multi-reference quantum mechanics, capturing valence and spin fluctuations of the 3d electrons. Our approach explains the stabilisation of the experimentally observed di-Cu singlet for the butterflied $${{\rm{Cu}}}_{2}{{\rm{O}}}_{2}$$ Cu 2 O 2 core, with localised charge and incoherent scattering processes across the oxo-bridge that prevent long-lived charge excitations. This suggests that the magnetic structure of hemocyanin is largely influenced by the many-body corrections.

Materials with strong electronic correlations host remarkable---and technologically relevant---phenomena such as magnetism, superconductivity, and metal-insulator transitions. Harnessing and controlling these effects is a major challenge, on which key advances are being made through lattice and strain engineering in thin films and heterostructures, leveraging the complex interplay between electronic and structural degrees of freedom. Here we show that the electronic structure of $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_{3}$ can be tuned by means of lattice engineering. We use different substrates to induce compressive and tensile biaxial epitaxial strain in $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_{3}$ thin films. Our measurements reveal systematic changes of the optical spectrum as a function of strain and, notably, an increase of the low-frequency free carrier weight as tensile strain is applied. Using density functional theory (DFT) calculations, we show that this apparently counterintuitive effect is due to a change of orientation of the oxygen octahedra. The calculations also reveal drastic changes of the electronic structure under strain, associated with a Fermi surface Lifshitz transition. We provide an online applet to explore these effects. The experimental value of integrated spectral weight below 2 eV is significantly (up to a factor of 3) smaller than the DFT results, indicating a transfer of spectral weight from the infrared to energies above 2 eV. The suppression of the free carrier weight and the transfer of spectral weight to high energies together indicate a correlation-induced band narrowing and free carrier mass enhancement due to electronic correlations. Our findings provide a promising avenue for the tuning and control of quantum materials employing lattice engineering.

Superconductivity in organic conductors is often tuned by the application of chemical or external pressure. With this type of tuning, orbital overlaps and electronic bandwidths are manipulated, whilst the properties of the molecular building blocks remain virtually unperturbed.Here, we show that the excitation of local molecular vibrations in the charge-transfer salt $\kappa-(BEDT-TTF)_2Cu[N(CN)_2]Br$ induces a colossal increase in carrier mobility and the opening of a superconducting-like optical gap. Both features track the density of quasi-particles of the equilibrium metal, and can be achieved up to a characteristic coherence temperature $T^* \approxeq 50 K$, far higher than the equilibrium transition temperature $T_C = 12.5 K$. Notably, the large optical gap achieved by photo-excitation is not observed in the equilibrium superconductor, pointing to a light induced state that is different from that obtained by cooling. First-principle calculations and model Hamiltonian dynamics predict a transient state with long-range pairing correlations, providing a possible physical scenario for photo-molecular superconductivity., Comment: 11 pages, 7 figures, supplementary material

This paper studies why doping a Mott insulator does not necessarily lead to a pseudogap in two dimensions. The authors propose a criterion for the appearance of strong-coupling pseudogap in the doped Hubbard model.

Layered perovskite ruthenium oxides exhibit a striking series of metal-insulator and magnetic-nonmagnetic phase transitions easily tuned by temperature, pressure, epitaxy, and nonlinear drive. In this work, we combine results from two complementary state-of-the-art many-body methods, auxiliary field quantum Monte Carlo and dynamical mean field theory, to determine the low-temperature phase diagram of ${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}$. Both methods predict a low-temperature, pressure-driven metal-insulator transition accompanied by a ferromagnetic-antiferromagnetic transition. The properties of the ferromagnetic state vary nonmonotonically with pressure and are dominated by the ruthenium ${d}_{xy}$ orbital, while the properties of the antiferromagnetic state are dominated by the ${d}_{xz}$ and ${d}_{yz}$ orbitals. Differences in the details of the predictions of the two methods are analyzed. This work is theoretically important as it presents the first application of the auxiliary field quantum Monte Carlo method to an orbitally degenerate system with both Mott and Hunds physics and provides an important comparison of the dynamical mean field and auxiliary field quantum Monte Carlo methods.